Global stability analysis of discrete-time coupled systems on networks and its applications

被引：61

作者：

Su, Huan ^{[1
]}

Li, Wenxue ^{[1
]}

Wang, Ke ^{[1
,2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China

[2] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

CHAOS | 2012年 / 22卷 / 03期

关键词：

GROSSBERG NEURAL-NETWORKS; FINITE-DIFFERENCE SCHEMES; EXPONENTIAL STABILITY; ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS; VARYING DELAYS; DYNAMICS; MODELS;

D O I：

10.1063/1.4748851

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the global stability for a general discrete-time coupled system on network (DTCSN). A systematic method of constructing global Lyapunov function for the DTCSN is provided by combining graph theory and the Lyapunov method. Consequently, some novel global stability principles, which have close relation to the topology property of the network, are given. They have important leading significance in the design and applications for the globally stable DTCSNs. In addition, to present the effectiveness and applicability of the results, the proposed theory is used to analyze the global stability for some practical models and numerical methods. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4748851]

引用

页数：11

共 32 条

[1] Stability analysis of nonlinear quadratic systems via polyhedral Lyapunov functions [J].

Amato, Francesco ;

Calabrese, Francesco ;

Cosentino, Carlo ;

Merola, Alessio .

AUTOMATICA, 2011, 47 (03) :614-617

[2] Stability of coupled map networks with delays [J].

Atay, Fatihcan M. ;

Karabacak, Oezkan .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2006, 5 (03) :508-527

[3] Map model for synchronization of systems of many coupled oscillators [J].

Barlev, Gilad ;

Girvan, Michelle ;

Ott, Edward .

CHAOS, 2010, 20 (02)

[4] Boundedness and stability for Cohen-Grossberg neural network with time-varying delays [J].

Cao, J ;

Liang, JL .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 296 (02) :665-685

[5] Adaptive synchronization of neural networks with or without time-varying delay [J].

Cao, JD ;

Lu, JQ .

CHAOS, 2006, 16 (01)

[6] Global asymptotic stability of delayed Cohen-Grossberg neural networks [J].

Chen, Y .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2006, 53 (02) :351-357

[7] ABSOLUTE STABILITY OF GLOBAL PATTERN-FORMATION AND PARALLEL MEMORY STORAGE BY COMPETITIVE NEURAL NETWORKS [J].

COHEN, MA ;

GROSSBERG, S .

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS, 1983, 13 (05) :815-826

[8]

Cull P., 2005, DIFFERENCE EQUATIONS

[9]

Elaydi S., 2004, INTRO DIFFERENCE EQU

[10] Basins of attraction in strongly damped coupled mechanical oscillators: A global example [J].

Fiedler, B ;

Belhaq, M ;

Houssni, M .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1999, 50 (02) :282-300

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